Review Modeling synthetic gene oscillators Erin L. O’Brien a , Elizabeth Van Itallie a , Matthew R. Bennett a,b,⇑ a Department of Biochemistry & Cell Biology, Rice Univeristy, 6100 Main St., Houston, TX, United States b Institute of Biosciences & Bioengineering, Rice Univeristy, 6100 Main St., Houston, TX, United States article info Article history: Received 8 August 2011 Received in revised form 5 January 2012 Accepted 6 January 2012 Available online 18 January 2012 Keywords: Synthetic biology Genetic oscillators Modeling Delay Transcriptional regulation Gene networks abstract Genetic oscillators have long held the fascination of experimental and theoretical synthetic biologists alike. From an experimental standpoint, the creation of synthetic gene oscillators represents a yardstick by which our ability to engineer synthetic gene circuits can be measured. For theorists, synthetic gene oscillators are a playground in which to test mathematical models for the dynamics of gene regulation. Historically, mathematical models of synthetic gene circuits have varied greatly. Often, the differences are determined by the level of biological detail included within each model, or which approximation scheme is used. In this review, we examine, in detail, how mathematical models of synthetic gene oscil- lators are derived and the biological processes that affect the dynamics of gene regulation. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction In order to perform the multitude of functions necessary to sur- vive, cells must be able to regulate the expression pattern of their genes [1]. Often, this is accomplished through genetic networks – intricate webs of interactions between regulatory elements con- trolling protein production. The topological similarities between gene networks and electronic devices have lead many to draw analogies between the two, and hence gene networks are often re- ferred to as ‘‘gene circuits’’ [2,3]. Coupled to this analogy is the be- lief that mathematical modeling of genetic networks will lead to new insights into their role in regulating cellular functions [4,5]. To better understand the regulatory mechanisms of gene net- works, both quantitatively and qualitatively, synthetic biologists construct small-scale systems that can be studied in fine detail [6,7]. Synthetic gene circuits are generally comprised of a few inter- acting genes that can be placed into organisms with minimal inter- ference from the hosts’ own regulatory processes. While naturally occurring gene networks are generally much more complicated, the simplicity of synthetic circuits provides a more manageable framework with which to test mathematical models. In addition, it is hoped that new, practical technologies will emerge from testing the limits of rationally engineered gene circuits. Indeed, the com- plexity of synthetic circuits and range of their functionality have greatly increased. For instance, synthetic gene circuits now exist with diverse behaviors, such as toggle switches [8], pulse counters [9], and image detectors [10,11]. One of the most studied types of synthetic gene circuits, how- ever, is the oscillator. These circuits are designed to produce peri- odic changes to the expression level of the target genes, in turn generating periodic changes in the concentration of the resulting proteins. To date there have been numerous synthetic gene oscilla- tors reported in the literature, beginning with the ‘‘repressilator’’ over a decade ago [12]. Since then, circuits displaying oscillatory behavior have evolved greatly and have displayed a host of inter- esting properties [13–22]. There are several reasons why synthetic gene oscillators have been so heavily studied. First, oscillations are an important natural phenomena observed in cellular life. For instance, the circadian rhythms and the eukaryotic cell cycle are controlled by genetic networks that act as oscillators [23,24]. Additionally, some stress response signaling pathways, such as the p53 and NF-jB pathways, can respond to stimuli with transient oscillations [25,26]. While the oscillations do not persist, the dynamical properties of the fluc- tuations can determine the specific downstream response [27]. Therefore, it is important that we understand how genetic oscilla- tions occur and how they are regulated in order to understand cel- lular physiology. The second reason, and perhaps the more important reason, that synthetic gene oscillators are studied is that they are simple circuits that nevertheless display rich dynamical behavior. This provides synthetic biologists with the opportunity to test mathe- matical theories of genetic regulation. 0025-5564/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.mbs.2012.01.001 ⇑ Corresponding author at: Department of Biochemistry & Cell Biology, Rice Univeristy, 6100 Main St., Houston, TX, United States. E-mail address: matthew.bennett@rice.edu (M.R. Bennett). Mathematical Biosciences 236 (2012) 1–15 Contents lists available at SciVerse ScienceDirect Mathematical Biosciences journal homepage: www.elsevier.com/locate/mbs